FOTD -- July 05, 2008 (Rating 6)
Fractal visionaries and enthusiasts:
With today's image I introduce the ultimate, final, absolutely
last version of the DivideBrot series of formulas -- version
number 5. It draws the same images as version 4, but with two
minor changes.
I have added a value of 0.00000000000000000001, or 10^-20, to
the imag(p1) parameter. This insignificant addition avoids a
blank screen when the parameter is set to zero, and has no
effect on the calculation time or image. I have also elimina-
ted the real(p2) parameter and inserted a hard-coded bailout
radius of 1,000,000, which eliminates the need to raise the
bailout as the imag(p1) parameter is increased. The result is a
simpler formula with less chances for mistakes.
I named today's image "Pancake With Syrup". (The syrup is
blueberry flavored.) I rated it at a 6, which indicates that
I do not consider it anything out of the ordinary.
The magnitude of the image is large enough to make the math-
tolerance entry necessary. This assures that the parameter file
calculates at the correct magnitude.
The parent fractal is another almost-Mandelbrot set, with
today's image located on a spike on the northeast shoreline of
the main bay of the large midget on the negative spike of the
parent M-set. As is true of many almost M-sets, the main bay as
well as the buds are filled with tiny bits of debris, which
prove to be entire universes when enlarged.
The calculation time of only 42 seconds exceeds the speed of
light, showing that the theory of relativity is flawed. The
completed GIF image is available on the FOTD web site at:
<http://home.att.net/~Paul.N.Lee/FotD/FotD.html>
While we were relaxing in our lawn chairs this afternoon, FL
casually asked me whether I believed in science or religion.
Not being in the mood for philosophical rambling, I replied that
I believe in both of them, since both science and religion are
real. This reply saved a lot of words, but I'm not sure what I
would have said if she had worded the question differently and
asked me whether I consider faith or reason to be the the better
path to ultimate truth. The question brought my philosophical
muse to life however, so expect some enlightening or not so
enlightening words about faith and reason before long.
Heavy clouds and threatening rain made Friday less than ideal at
Fractal Central. And the temperature of 73F 23C hardly felt
like Independence Day, which is usually as hot as a firecracker.
But it stayed dry, the neighborhood cookouts were a success, and
the fractal cats made the most of the marginal conditions.
The next FOTD will be posted in 24 hours. Until then, take
care, and watch for runaway fractals.
Jim Muth
jamth(a)mindspring.com
jimmuth(a)aol.com
START PARAMETER FILE=======================================
Pancake_With_Syrup { ; time=0:00:42.81-SF5 on P4-2000
reset=2004 type=formula formulafile=allinone.frm
formulaname=DivideBrot5 center-mag=-10.45034361189\
851/+0.00241713891946783/2.225036e+012/1.001
params=6/6 float=y maxiter=1500 inside=0 logmap=105
periodicity=10 mathtolerance=0.05/1
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bUz_WzYazUgzR8zb4zd0ze5zb }
frm:DivideBrot5 { ; Jim Muth
z=0, c=pixel, a=real(p1)-2,
b=imag(p1)+0.00000000000000000001:
z=sqr(z)/(z^(-a)+b)+c
|z| < 1000000 }
END PARAMETER FILE=========================================
FOTD -- July 04, 2008 (Rating 8)
Fractal visionaries and enthusiasts:
In a recent letter to the Fractint list, JoTz noticed that the
parent fractal of the "Order Septemdecem" FOTD image, which
resembles a Mandelbrot set and was posted on June 27, has a bit
of unexpected detail in its interior. I have known about this
extra stuff since I started working on the DivideBrot formulas.
The extra detail in the parent of the septemdecem fractal is
actually the fragmentary remains of a Z^17+C Mandeloid, which
appears when the imag(p1) parameter is set very close to but not
exactly at zero. (I usually use the number 0.0000000001 instead
of zero. In this case, the exponential form [1e-010] inserted
in the formula does not work. This will be corrected in version
number 5.)
When imag(p1) is set to virtually zero, the resulting fractal is
the normal Z^17+C Mandeloid. But as imag(p1) is increased, this
Mandeloid gradually grows in size and morphs into the tradition-
al Mandelbrot set, leaving order-17 debris to dissolve in the
interior of the forming M-set. Some of the intermediate steps
are quite interesting, but due to the size change, an animation
with consistently sized elements would be difficult.
The basic rule is: the smaller the value of imag(p1) the smaller
the size of the resulting fractal and the more prominent the
higher order shape, while at the same time, the greater the
value of imag(p1) the larger the size of the resulting fractal
and the more prominent the classic Mandelbrot-set shape.
Today's scene takes advantage of the dissolving high-order
debris in the center of the main bay of the parent 'almost-a-
Mandelbrot set'. The scene is located in what first appears as
a tiny dot, but when blown up reveals itself as an entire
fractal universe.
Due to the unusually large magnitude of the image, an outzoom
to the parent fractal is quite a trip, but very interesting.
But be sure to turn off the logmap feature before taking the
backwards trip.
BTW, the DivideBrot4 formula will soon be superseded by the
DivideBrot5 formula, which will be used for all future fractals
of today's type.
I rated today's image, which shows an unusually well-defined
cubic minibrot, at an 8. It's worth it. I named it "Perfectly
Cubic" for the same reason.
The calculation time of 47 seconds will cause no pain to those
with computers that are not over-qualified. Those with machines
that can surf the web in a flash but cannot run Fractint may
still see the image by visiting the FOTD web site at:
<http://home.att.net/~Paul.N.Lee/FotD/FotD.html>
and enjoying there the image that Paul calculated.
Lots of clouds, only a little sunshine, high humidity, a tempera-
ture of 84F 29C, and a threat of rain followed by actual rain,
made Thursday less than ideal here at Fractal Central. Not
concerned with weather, the fractal cats spent a good part of
the day trying to catch a fly. When one of them eventually
caught it, the exhausted duo settled down to sleep.
My day was busy, mostly because tomorrow is a holiday. The FOTD
does not take time off for holidays however, and will be posted
on schedule in 24 hours.
Jim Muth
jamth(a)mindspring.com
jimmuth(a)aol.com
START PARAMETER FILE=======================================
Perfectly_Cubic { ; time=0:00:47.85-SF5 on P4-2000
reset=2004 type=formula formulafile=allinone.frm
formulaname=DivideBrot4 passes=1 center-mag=-0.606\
3981173832952/+0.006169462807566/5.040456e+012/1/\
-83.80/0 params=3/3/3/0 maxiter=1000 logmap=58
float=y inside=0 periodicity=9 mathtolerance=0.05/1
colors=00097UAAWBDYCG_DJaEMcFPeGSgHViIZkKbmMfoOkqQ\
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vuzwvzywzzrztnzniziezcQzk }
frm:DivideBrot4 { ; Jim Muth
z=0, c=pixel, a=real(p1)-2,
b=imag(p1), d=real(p2)+100:
z=sqr(z)/(z^(-a)+b)+c
|z| < d }
END PARAMETER FILE=========================================
FOTD -- July 02, 2008 (Not Rated)
Fractal visionaries and enthusiasts:
Because of a big rush that we expect in, I will post no FOTD for
July 3. The FOTD for July 4 will return on or near schedule.
Today's image lies in the fractal that results when the formula
Z^sqrt(2)+C is iterated 5 levels up the logarithmic spiral when
the function 'one' is applied. Actually, I'm not convinced that
this is a function at all, but it makes some rather interesting
fractals, so we'll let it go.
This parent fractal resembles nothing as much as a duck with a
turned-up bill. Today's scene is located far out on a filament
extending eastward from the duck's breast.
I named the image "Creepy Crawlies" because of the cloud of
hairy filaments surrounding the sorry excuse of a minibrot at
the center. But try as I might, I could not decide on a rating.
The calculation time of 1-1/2 minutes if fast enough to keep
everyone happy. Happiness may also be found on the FOTD web
site at:
<http://home.att.net/~Paul.N.Lee/FotD/FotD.html>
where the completed image is posted.
The Tuesday weather was totally perfect here at Fractal Central.
The fractal cats enjoyed the near perfection to the utmost. My
day was busier than usual due to squeezing three days' work into
one day. Since there will be no FOTD for July 3, the next FOTD
will appear in 48 hours. Until 2 days have passed, take care,
and be eager to discover the next fractal.
Jim Muth
jamth(a)mindspring.com
jimmuth(a)aol.com
START PARAMETER FILE=======================================
Creepy_Crawlies { ; time=0:01:34.27-SF5 on P4-2000
reset=2004 type=formula formulafile=allinone.frm
formulaname=MandelbrotBC3 function=one passes=1
center-mag=+1.126434310277434/-0.0602249097173638/\
1.282804e+008/1/-35/0 params=1.4142/0/5/0 float=y
maxiter=2500 inside=0 periodicity=10
colors=000bXYbXZbX_bY`bYabYbbYcbYccYbcYacYacY`dY_d\
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frm:MandelbrotBC3 { ; by several Fractint users
e=p1, a=imag(p2)+100
p=real(p2)+PI
q=2*PI*fn1(p/(2*PI))
r=real(p2)+PI-q
Z=C=Pixel:
Z=log(Z)
IF(imag(Z)>r)
Z=Z+flip(2*PI)
ENDIF
Z=exp(e*(Z+flip(q)))+C
|Z|<a }
END PARAMETER FILE=========================================
.
Zoom-in to FOTD 27-06-08 is posted.
WMV, 640x480, 41 sec, 10 Meg.
http://www.fractal-animation.net/vid/order_septemdecem.zip
.
Strange. If you zoom out to the parent fractal it looks pretty much like an ordinary mandelbrot.
But you see a few lit pixels - single pixels - in the main black lake, especially the secondary bulb.
I thought it was a monitor glitch or video artifact, but if you zoom in you see detail and structure.
Whatsup with that?
Stay amazed!
JoTz
.
FOTD -- July 01, 2008 (Rating 6)
Fractal visionaries and enthusiasts:
In today's FOTD we continue the investigation of higher order
minibrots in apparent classic Mandelbrot sets. Today's order-7
minibrot was found in the star of a high-order bud rather deep
in the East Valley of its parent.
To add a bit of oomph to an otherwise routine image I rendered
it with the outside set to 'tdis', which is really quite useful
when no other coloring options seem to work.
But even with the 'tdis' outside the image rates only a 6. This
is not too bad, but I would like to have a rating a bit higher.
I named the image "Feeling Testy", which has nothing to do with
my mood. The words simply came to mind as I studied the scene.
In comparison with yesterday's image, which calculates in 20
seconds, today's image takes almost 9 minutes to finish. To
ease impatience, I recommend going to the FOTD web site at:
<http://home.att.net/~Paul.N.Lee/FotD/FotD.html>
and viewing the finished image there.
Monday turned out quite pleasant here at Fractal Central, with
enough sun to keep everyone happy and a temperature of 82F 28C,
which was made quite comfortable by the lower humidity. The
fractal cats agreed. A moderate thunder-shower came up at 9pm
to end the day with a bang.
My day was very average. I only hope tomorrow can be the same.
The next FOTD will appear in 24 hours. Until then, take care,
and if you know it and know that you know it, then you know it
is true.
Jim Muth
jamth(a)mindspring.com
jimmuth(a)aol.com
START PARAMETER FILE=======================================
Feeling_Testy { ; time=0:08:52.83-SF5 on P4-2000
reset=2004 type=formula formulafile=allinone.frm
formulaname=DivideBrot4 passes=1
center-mag=+1.791011102984003/-0.0049543843970271/\
8.664403e+007/1/12.5/0 params=7/7/500/0 float=y
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UzrSzsSzsQzuQzuOzvOzvMzwM }
frm:DivideBrot4 { ; Jim Muth
z=0, c=pixel, a=real(p1)-2,
b=imag(p1), d=real(p2)+100:
z=sqr(z)/(z^(-a)+b)+c
|z| < d }
END PARAMETER FILE=========================================
